I have a path with a black fill that has two curves that meet at a point. I also have a vertical line that connects the beaks of both curves. How can I combine them so the right white triangle disappears and is replaced with black?)
Object > Expand...
Window > Pathfinder)
In case your curved shape had a stroke, that stroke will disappear when you unite. In this case, you need to expand the original shape, yielding its stroke and its fill as separate shapes. Unite those, and unite the expanded stroke with the resulting shape.